Problem: Simplify the following expression: $p = \dfrac{r}{5} + \dfrac{3r}{7}$
Explanation: In order to add expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $5$ and $7$ $\lcm(5, 7) = 35$ $ p = \dfrac{7}{7} \cdot \dfrac{r}{5} + \dfrac{5}{5} \cdot \dfrac{3r}{7} $ $p = \dfrac{7r}{35} + \dfrac{15r}{35}$ $p = \dfrac{7r +15r}{35}$ $p = \dfrac{22r}{35}$